# Temperature significant fig.

## Homework Statement

Convert 62.0 °C to Fahrenheit

°F=1.8(°C) +32

## The Attempt at a Solution

°F=1.8(62.0) + 32 = 143.60

I am confused on the significant figures for the answer. Does the temperature equal 143.6°F because 32 is an exact number?
Or 144°F because 32 is not exact (part of temperature conversion formula)?

In the book (Chemistry Tro 6th edition) Exact numbers include "Integral numbers that are part of an equation" such as
radius =diameter/2, the number 2 is exact.

thanks

symbolipoint
Homework Helper
Gold Member
I would assume 32 F is to three significant figures and that the 1.8 factor is also three (or more?) significant figures. I would keep three significant figures in the answer.

Borek
Mentor
In this case 32 and 1.8 are exact numbers (with an infinite number of significant zeros).

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symbolipoint
Homework Helper
Gold Member
In this case 32 and 1.8 are exact numbers (with an infinite number of significant zeros).
Worth going with that.
The temperature values themselves are measurements, so you would go only as far as how they are reported or given.

Ok 32 and 1.8 are exact numbers. So when I first multiply and then add will it become 143.6°F or 144°F? I thought it might be 143.6 because, even though the numbers are exact, the final step is adding (basing on decimal places). Or is it based on initial significant figures with the temperature starting with 3 significant digits.

symbolipoint
Homework Helper
Gold Member
Ok 32 and 1.8 are exact numbers. So when I first multiply and then add will it become 143.6°F or 144°F? I thought it might be 143.6 because, even though the numbers are exact, the final step is adding (basing on decimal places). Or is it based on initial significant figures with the temperature starting with 3 significant digits.
°F=1.8(62.0) + 32 =

Infinite sigfigs on 1.8 and on 32 but only 3 sigfigs on 62.0

F=111.6+32.000000000000000000

F=143.6

It is fair to say 143.6, but probably better to view the computation going as F=112+32.00000=144;
the first term became limited to 3 significant figures, so adding the next term should not change that.
Better then, to say F=144

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Thank you! I got it.